I'm going to address this from a different angle, which may or may not sound good.. Have you ever been in love? If yes, does that prove love exist? If no, does it prove it doesn't?
It's already been pointed out that it depends on the individual's interpretation of the experience. Someone who think's they're in love with the greatest person in the world would obviously have to believe love exists, and the person who's jaded and cynical about love may very well deny the fact that others care about them, in whatever shape or form that may take.
Things like this will often be misinterpreted too. On the rare occasions where I discuss the principles behind internal martial arts with people who are not familiar with it, I find people who are not familiar with it have a tendancy to interpret the phenomenon as psychokinesis, which it is not, and none of the practitioners think of it in that way. But there are people who question whether it actually exists, too, and of course that comes from their own experience base and what they believe based on people they know etc. In this case, to have the experience would either mean you develop the ability yourself, which people will readily tell you take a long time, or you can be on the receiving end and get hurt. So... In a way it's kind of a catch 22, but people who fancy themselves as tough guys have gotten hurt before.
I think I've said it before, but the interesting thing about this kind of stuff is that all the teaching and teachers who seems to be most authentic to me will tell you to meditate in some way, and the common ingredient in the meditations is to think of nothing or cling to nothing, not even the belief that it is true, I can do it, I believe in myself or any of that crap. Maybe that is what is hard, or atleast rare - for people to completely drop all of their assumptions, even for just a moment.